There are dominantly three models in so-called contemporary jazz. They perform as frameworks for understanding the behavioral dynamics of an ensemble comprised of soloists and rhythm section organized according to the trope of “improvisation” (in addition to more obvious idiomatic controls). In each case “improvisation” is construed voluntaristically, reactively, or at level of individuation (compulsory). Present characterizations are provisional. The author of the present text does not purport to be communicating on any sort of behalf.

  1. Classical: Yes or No
  1. Trivialist: Yes and Yes
  1. Intuitionist: Yes and No

The classical model draws distinction between soloist and rhythm section. Latter is determined by structure albeit not determined by rhythm section, which conserves structure (e.g. ‘theme and variations/head-in, head-out’). Thus, soloist voluntarily proceeds without reactive bias towards rhythm section — a basal, primitive layer — but rather biases towards implementation of structure as representational determiner. One solos as if the catalytic agent is the structure and thereby references it as such. Performance determined by such structure is then necessarily a computational formalist insofar as one is not observing the agent of representation (soloist) but that which is represented independent of it (solo). Exemplified by Tristano School: Marsh, Mosca, Crothers (circa Perception), Ball, et. al. (Also cf. this article for the humanist equivocations of computational formalism with “coldness” and descriptions of Tristano’s organizational culture for ensembles.) Arguably, Holdsworth and morphologically-similar ‘fusion’ implicitly endorses this model, as well as much ‘crossover’ (Rippingtons, Koz, Dulfer, James, etc.).
The trivialist model subtracts the role of structural conservation agent for the trivialization of soloist (i.e. “everyone is soloing”) wherein reactivity is collectively based upon the (inductively) non-hierarchical organization of performers (’soloists’) rather than structure (insofar as it has been subtracted). Structure is ignored in favor of reacting to those that would conserve structure. Since disorganization and depletion of conservation is emphasized, the ‘democracy’ or ‘radical equality’ of the trivialist model yields strong homogeneity, or, thermodynamically-speaking, heat death. Hence why, at the peak of so-called “free jazz,” many claimed jazz to be dead (e.g. Tynan 1962): everyone performing was, logically, dead. Exemplified by Ayler, Taylor, Mazzolaet. al.
The intuitionist (or ‘revisionist’) model conserves the classical stipulation of structural determination and law of excluded middle with regard to performer organization (i.e. one is either soloing or not, lost or not, etc). However, the locus of revision to the classical model lies in either a bias towards reactivity between performers for purposes of collective (rather than particular) individuation. Individuation is collective insofar as agents of conservation are also permitted structural deviations that are either determined (referential) by or ignorable (non-referential) for structure. Referential or non-referential events yielded by ensemble performers are equally probable. Exemplified by Braxton (e.g. GTM and Quintet (Tristano) 1997), Konitz-Mehldau-Haden-Motian, Lacy, et. al
(The historical-musicological stagnation of deploying early-mid 20th century compositional paradigms indicative of all three models will not be discussed. This much should be said, for now: in terms of the musicological — and thus cultural — influence of ‘jazz’, its appearance under such a boundary is wholly minimal … or at least has been usurped and consequently abstracted and generalized in principles by regional genres. One proposed mechanism for the non-appearance of this ‘influence’ may be due to such musicological stagnation. Which of course defers to the overarching saturation of empirical trivialism — ”everything is true as x” — and product yield — indexing extant and imminent resource depletion, range contraction, species richness and diversity disappearance (dis-orientation?) — predominant in ‘contemporary musicology’. Many people, when this is the case, just say, “It’s finished.” And really, a musicological sequence has a beginning and an end, too, an end in the form of saturation. Saturation is not a brutal rupture, but it becomes progressively more difficult to find something new in the field of the fidelity.)
One is ambivalent to propose an alternative, as it is just as indexical to the saturation of not only these models but the mode under which the present writing ‘takes place’, generically. The proposal of an alternative, in its conditions of positing, is not only ideological, idealist, but disgusting. One can only admit (resign) that they have no capacity to propose an alternative, nor affirm there is no alternative. However, one may be posited under conditions of self-refutation. On a personal albeit not unrelated note, it is quite painful to write the present text, as I have carpal tunnel. The bias to exteriorize is truly abhorrent. 
A potential alternative to the aforementioned models is what may be termed the skeptical model. Such a model is perhaps no more a synthesis of, predictably (necessarily?), classical and trivialist, focusing principally on the determinism of the former and homogeneity (qua fatalism) of the latter. What this might entail (if anything … which is to say, the hypothesis is that it will not … null as alternative) that the soloist agentially replicates the role of conservator — thus wholly (‘vulgarly’?) determined by structure — while having no capacity to deviate from (ignore qua individuate) or react (conform?) to variations indexical to the structure — thus homogenous and suspended from systematic exchange. This latter point shifts the locus of subtraction (willfully ignoring) of structure performed via soloist to the locus of deviation itself as essential to their role as soloist. in other words, rather than subtracting the structure that determines their events, the essence of their yield is subtracted. But, is this to say that, in the syntax of the trivialist, “everyone is just a rhythm section agent?” Before providing a possible resolution, I’ll also remind you that, in the case of the Tristano school method which subtracts the theme and variations structure — i.e. not stating any theme, but only variation — we get results like Jazz from the East Village or The Art of Improvising (Marsh), where every track, a posteriori, yields near morphological, qualitative, and quantitative triviality, engaging contiguity with the purported object of their suppression (much like the trivialist, naturally). 
Which isn’t to leave the intuitionist as an unproblematic figure, either. Isn’t the induction of ‘rationally’ or even worse, ‘intentionally’ instantiating the supposed conditions of collective or personal individuation peak dogmatism? One might think. Not to mention that the voluntarism inherent in the conditions that render even such a ‘choice’ possible not only lapses into the boundless death of the trivialist, but also the confidence in ultimately illusory (by default) notions such as ‘self’ and ‘aesthetic’. The totally uncritical ideology surrounding the culture of reactivity and interactivity, not to mention antiquated principles of narrative ‘development’ and ‘organic’ vitality undergirding the practice of so-called ‘jazz’, is like an epidemic that only yields zombification. Is this “bad?” Not in the least. More significantly, it only, in the last instance, yields the least. This is the hinge of the skeptical model, except with any mechanism of entailment suspended. 
The skeptical model might preserve the static determinism of structural dependence — and, crucially, without contingency upon the performer’s knowledge or belief in that structure … which is to permit the condition of one unconditionally and unfreely blindly sightreading — inherent to the classical model, as well as the static homogeneity and suspension of non-trivial yield inherent to the trivial model. In other words, we have the structure of ‘theme’, without variation, albeit without the freedom to purchase the theme’s property. This might amount to each performer only positing trivialities with respect to each other’s proposition, as well as the determining structure, unconditionally and independent of dynamics (i.e. possibility).
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